Details

analyze350.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.1s (21.1%)

Results

757.0ms	7151×	body	128	valid
103.0ms	427×	body	512	valid
102.0ms	336×	body	1024	valid
62.0ms	306×	body	256	valid
12.0ms	36×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify133.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

9.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.2b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	13.8b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	3.5b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series67.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

47.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
20.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

7.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

simplify121.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
644×	`fma-neg_binary64`
523×	`cancel-sign-sub-inv_binary64`
397×	`sub-neg_binary64`
195×	`div-sub_binary64`

Counts

160 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4255
1	740	4157
2	2480	3550
3	4430	3531
4	5167	3531

prune121.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	132	7	139

Error

0.0b

Counts

139 → 7

Alt Table

Status	Error	Program
	13.8b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
▶	10.2b	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
	33.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.9b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	10.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	24.2b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	31.7b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 3612 to 1222 computations (66.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))))
	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	2.0b	(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))
✓	2.2b	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))

series131.0ms (2.5%)

Counts

3 → 168

Calls

3 calls:

49.0ms	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
47.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))))
35.0ms	(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
31×	`associate-r_binary64`
26×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`

Counts

3 → 87

Calls

3 calls:

12.0ms	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
11.0ms	(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))))

simplify198.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

617×	`sub-neg_binary64`
455×	`fma-neg_binary64`
281×	`associate--r+_binary64`
235×	`associate--l+_binary64`
214×	`+-commutative_binary64`

Counts

255 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	6826
1	976	6577
2	3775	5912
3	4796	5912
4	4993	5912
5	4969	5912

prune229.0ms (4.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	310	2	312
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	311	8	319

Error

0.0b

Counts

319 → 8

Alt Table

Status	Error	Program
	48.2b	(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) 3)) (fma.f64 y y (*.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) (-.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) y))))
	33.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.9b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
▶	10.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	24.2b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	13.9b	(+.f64 y (+.f64 x (.f64 (.f64 y (-.f64 t z)) (/.f64 1 (-.f64 a t)))))
	31.7b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	13.8b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 8730 to 2627 computations (69.9% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 t z))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
✓	3.5b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))

series85.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
23.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
21.0ms	(/.f64 (-.f64 a t) (-.f64 t z))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/.f64 (-.f64 a t) (-.f64 t z))
9.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))

simplify184.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

672×	`cancel-sign-sub-inv_binary64`
565×	`sub-neg_binary64`
292×	`fma-neg_binary64`
225×	`+-commutative_binary64`
218×	`associate--r+_binary64`

Counts

346 → 344

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	8897
1	1039	8416
2	3680	8214
3	5459	8214

prune252.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	344	8	352

Error

0.0b

Counts

352 → 8

Alt Table

Status	Error	Program
	48.2b	(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) 3)) (fma.f64 y y (*.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) (-.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) y))))
	33.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.9b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	10.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	24.2b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	13.9b	(+.f64 y (+.f64 x (.f64 (.f64 y (-.f64 t z)) (/.f64 1 (-.f64 a t)))))
	31.7b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
▶	13.8b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 9555 to 2919 computations (69.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 z t) y)
✓	2.2b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	9.7b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

series93.0ms (1.8%)

Counts

3 → 120

Calls

3 calls:

50.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
36.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
7.0ms	(*.f64 (-.f64 z t) y)

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
44×	`prod-diff_binary64`
30×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`

Counts

3 → 134

Calls

3 calls:

10.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
8.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
5.0ms	(*.f64 (-.f64 z t) y)

simplify159.0ms (3%)

Algorithm

1×	egg-herbie

Rules

375×	`fma-neg_binary64`
215×	`associate--l+_binary64`
205×	`associate-/l*_binary64`
202×	`+-commutative_binary64`
165×	`associate-l_binary64`

Counts

254 → 252

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	409	8984
1	1155	7136
2	4503	7136
3	5025	7136

prune301.0ms (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	254	6	260

Error

0.0b

Counts

260 → 6

Alt Table

Status	Error	Program
	17.6b	(+.f64 (fma.f64 1 (+.f64 x y) (neg.f64 (.f64 (/.f64 y (-.f64 a t)) (/.f64 (-.f64 z t) 1)))) (fma.f64 (neg.f64 (/.f64 y (-.f64 a t))) (/.f64 (-.f64 z t) 1) (.f64 (/.f64 y (-.f64 a t)) (/.f64 (-.f64 z t) 1))))
	31.7b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	33.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.9b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	10.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	13.9b	(+.f64 y (+.f64 x (.f64 (.f64 y (-.f64 t z)) (/.f64 1 (-.f64 a t)))))

Compiler

Compiled 7927 to 1812 computations (77.1% saved)

regimes1.3s (24.6%)

Accuracy

Total 5.9b remaining (99.3%)

Threshold costs 0b (0%)

Counts

127 → 6

Compiler

Compiled 14842 to 8957 computations (39.7% saved)

bsearch104.0ms (2%)

Steps

Iters	Range		Point
9	1.9770623501210711e+105	2.380957886296455e+112	6.631897434957769e+108
8	2.350251294037788e-107	7.250650772986426e-105	7.085746189680331e-107
9	-3.2601611583991704e+75	-6.065792701712438e+66	-1.8329458807432838e+68
5	-2.5917063064749753e+129	-6.923147579429955e+128	-1.1983208753291875e+129
8	-2.1327617301420188e+172	-1.516850214832903e+168	-1.9658820839659733e+171

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
14×	`sub-neg_binary64`
13×	`*-commutative_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	144
1	66	144
2	92	144
3	114	144
4	137	144
5	146	144
6	147	144
7	143	144

end138.0ms (2.6%)

Compiler: Compiled 353 to 160 computations (54.7% saved)

Details

analyze350.0ms (6.7%)

sample1.1s (21.1%)

simplify133.0ms (2.5%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series67.0ms (1.3%)

rewrite11.0ms (0.2%)

simplify121.0ms (2.3%)

prune121.0ms (2.3%)

localize10.0ms (0.2%)

series131.0ms (2.5%)

rewrite34.0ms (0.6%)

simplify198.0ms (3.8%)

prune229.0ms (4.4%)

localize10.0ms (0.2%)

series85.0ms (1.6%)

rewrite45.0ms (0.9%)

simplify184.0ms (3.5%)

prune252.0ms (4.8%)

localize9.0ms (0.2%)

series93.0ms (1.8%)

rewrite36.0ms (0.7%)

simplify159.0ms (3%)

prune301.0ms (5.8%)

regimes1.3s (24.6%)

bsearch104.0ms (2%)

simplify8.0ms (0.1%)

end138.0ms (2.6%)

Profiling